A student constructed a triangle with the known conditions to him bein

1.	A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows: 1. Draw a line segment, say XY equal to AB + BC + AC 2. Make angles LXY equal to ∠ B and MYX equal to ∠ C 3. Bisect ∠ LXY and ∠ MXY. Let these bisectors intersect each other at A. 4. Draw perpendicular bisectors PQ of AX and RS of AY 5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC. 6. The triangle ABC is thus formed. How many isosceles triangles are there in this figure?
Answer» A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows: 1. Draw a line segment, say XY equal to AB + BC + AC 2. Make angles LXY equal to $∠$ B and MYX equal to $∠$ C 3. Bisect $∠$ LXY and $∠$ MXY. Let these bisectors intersect each other at A. 4. Draw perpendicular bisectors PQ of AX and RS of AY 5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC. 6. The triangle ABC is thus formed. How many isosceles triangles are there in this figure?

A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows: 1. Draw a line segment, say XY equal to AB + BC + AC 2. Make angles LXY equal to ∠ B and MYX equal to ∠ C 3. Bisect ∠ LXY and ∠ MXY. Let these bisectors intersect each other at A. 4. Draw perpendicular bisectors PQ of AX and RS of AY 5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC. 6. The triangle ABC is thus formed. How many isosceles triangles are there in this figure?

Answer»

A student constructed a triangle with the known conditions to him being the perimeter of the triangle and both the base angles. The steps of construction he used are as follows:

1. Draw a line segment, say XY equal to AB + BC + AC

2. Make angles LXY equal to $∠$ B and MYX equal to $∠$ C

3. Bisect $∠$ LXY and $∠$ MXY. Let these bisectors intersect each other at A.

4. Draw perpendicular bisectors PQ of AX and RS of AY

5. Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC.

6. The triangle ABC is thus formed.

How many isosceles triangles are there in this figure?

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